Problem: The grades on a language midterm at Loyola are normally distributed with $\mu = 66$ and $\sigma = 3.5$. Vanessa earned a $64$ on the exam. Find the z-score for Vanessa's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Vanessa's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{64 - {66}}{{3.5}}} $ ${ z \approx -0.57}$ The z-score is $-0.57$. In other words, Vanessa's score was $0.57$ standard deviations below the mean.